Persistence Fidelity Condition

The Persistence Fidelity Condition is the memory requirement that a quantum state's overlap with its own later self stays above a set fidelity threshold for as long as recursive processing needs to remember it. It belongs to the Temporal Persistence Requirements, alongside the Memory Depth Requirement: memory depth fixes how many processing steps must be spanned, and the persistence condition fixes how faithfully the state must survive that span. Measured as the time-evolved overlap of a state with itself, it sets the threshold for sustained quantum state preservation, which the book treats as critical for recursive information processing in substrate architectures. |⟨ψ(t)|ψ(t+τ)⟩|² ≥ F𝓜, where ⟨|⟩ is the quantum inner product, ψ(t) is the quantum state at time t, t is the initial time, τ is the time interval, bounded by τ ≤ N𝓕 × t⥂, and F𝓜 is the persistence fidelity threshold, given as 0.95 ± 0.02. t and τ carry [𝕋]; the overlap and the threshold are [∅], so the condition compares [∅] ≥ [∅]. It pairs with the Memory Depth Requirement and feeds PulseCore Validation Requirements, alongside Quantum Pulse Fidelity and Recursive Fidelity Decay.